Corresponding medians of congruent triangles are congruent.
1. Triangle ABC = Triangle DEF 1. Given.
2. Draw medians BP and EG. 2. Definition of median.
3. AB = DE 3. Corresponding parts theorem.
4. / A = / D. 4. Corresponding parts theorem.
5. AC = DF. 5. Corresponding parts theorem.
6. AP = (1/2)AC. 6. Definition of median.
7. DG = (1/2)DF. 7. Definition of median.
8. (1/2)AC = (1/2)DF. 8. Multiplication Property.
9. AP = DG. 9. Substitution.
10. Triangle ABP = Triangle DEG 10. SAS
11. BP = DG. 11. Corresponding Parts Theorem.